Leipzig, second in the Bundesliga, warmed up for Tuesday's key Champions League clash at home to Manchester United by pushing the European champions hard at the Allianz Arena.
"We knew before the game that we could come back, but the fact we had to do it was news to us," said Mueller.
"At the end of the day, we can live with the result."
Christopher Nkunku's early goal for Leipzig was cancelled out by a superb equaliser from Jamal Musiala, 17, before Mueller tapped home to put Bayern 2-1 up.
However, the lead lasted barely a minute as Justin Kluivert -- son of former Dutch star Patrick Kluivert -- levelled before half-time with his first goal for Leipzig.
A thumping Emil Forsberg header from an Angelino cross put visitors Leipzig 3-2 ahead soon after the break.
Bayern took a share of the points when Kingsley Coman produced a towering cross -- his third assist of the night -- for Mueller to head home the equaliser on 75 minutes.
"That really was a top game between two teams who really wanted to win," said Forsberg.
"It was awesome to be out there on the pitch - you live for games like that."
The result leaves Bayern two points clear at the top and Leipzig still waiting for a first win in Munich, after five attempts.
Dortmund drop points
Earlier, Borussia Dortmund dropped more points as they laboured to a 1-1 draw at Eintracht Frankfurt with star striker Erling Braut Haaland sidelined.
The result left Dortmund third in the table, four points behind Bayern.
After suffering a shock 2-1 home defeat last weekend against struggling Cologne, Dortmund missed the finishing of top scorer Haaland, who is out until January with a leg injury.
Dortmund's defence was caught napping when they conceded an early goal by Frankfurt's Japan midfielder Daichi Kamada.
Dortmund raised their tempo and equalised with a superb strike from 18-year-old US forward Giovanni Reyna, but they failed to breach the Frankfurt defence again despite finishing the stronger.
Borussia Moenchengladbach, who will try and clinch a place in the Champions League last 16 next week away to Real Madrid, drew 2-2 draw at Freiburg, where they have not won since 2002.
Gladbach went ahead when Swiss striker Breel Embolo netted with an excellent first-time shot on 23 minutes.
Freiburg equalised with a header by defender Philipp Lienhart and then took the lead just after the break when Vincenzo Grifo converted a penalty.
Gladbach levelled when Alassane Plea hit the top corner of the net with a wonderful curling shot on 50 minutes.
The result leaves Freiburg 14th, a point from the bottom three, while Gladbach are seventh and are seven points behind Bayern.
Having ended their 18-match winless run by shocking Dortmund 2-1 last weekend, Cologne backed it up with a 2-2 draw at home with Wolfsburg to climb to 15th.
Cologne's 18-year-old striker Jan Thielmann opened the scoring, but Maximilian Arnold equalised with a magnificent free-kick.
Winger Ondrej Duda restored Cologne's lead when he shot into the corner on 43 minutes, but Wout Weghorst rescued a point away for Wolfsburg just after the break.
Cologne are only out of the relegation places on goal difference while Wolfsburg are fifth.
Arminia Bielefeld earned their first win since September with a 2-1 victory at Mainz, although both clubs remain in the bottom three.
Sixth-placed Union expect to be without in-form striker Max Kruse for the foreseeable future after the 32-year-old injured his hamstring in Friday's 3-1 derby defeat at Hertha Berlin.
Kerem Demirbay will miss Bayer Leverkusen's game at bottom side Schalke on Sunday after the midfielder was quarantined after testing positive for Covid-19.
The rest of the Leverkusen squad have returned negative tests, the club confirmed.